plo quickstats final - amazon s3quickstats+final.pdf · without quickpro llc, and/or plo...

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FLOP EQUITYFLOP EQUITY

ONE PAIR MATCH-UPS

OVERPAIR VS TWO PAIR (~30/70) Board

Q♠ 9♣ 2♦ Hand Equity Q2** 71.06% AA** 28.94%

BARE OVERPAIR VS BARE TOP TWO Board

K♠ 9♣ 6♦ Hand Equity

K♠9♥3♣2♠ 73.54% A♥A♠7♥2♣ 26.46%

Commentary: Each back-door flush draw (BDFD) adds ~ 2.50% (A♦A♠7♦2♠ 32.44%). Unlikely back-door straight draws add ~1.00% (A♦A♠J♦5♠ 33.78%). More likely back-door straight draw adds ~3.50% (A♦A♠5♦4♠ 36.10%). Gut-shot adds ~11.0-15.0%, depending on how many back-door straight draws it has.

OVERPAIR + GUTSHOT + 2 BDFD + BDSD VS BARE TOP TWO PAIR Board

K♠ 9♣ 6♦ Hand Equity

K♣9♥3♠2♥ 54.51% A♠A♣7♣5♠ 45.49%

Commentary: To be flipping/slightly ahead of two pair on a rainbow board you basically need two back-door flush draws and an OESD.

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OVERPAIR VS PAIR + 3 LIVE SIDECARDS (~60/40) Board

K♣ 7♦ 6♠ Hand Equity AA23 58.95% KQJ8 41.05%

OVERPAIR VS PAIR + FD (~35/65) Board

6♥ 8♥ 2♠ Hand Equity

A♠A♦K♥4♣ 30.00% J♥T♥7♠6♦ 70.00%

OVERPAIR + FD VS PAIR + SIDECARDS + OESD (~60/40) Board

8♦ 9♠ 2♠ Hand Equity

A♠A♣K♠3♣ 60.49% J♦T♠9♣4♣ 39.51%

OVERPAIR + FD VS SET (~35/65) Board


K♠Q♠K♣7♦ 34.76% 9♣9♦8♣6♥ 65.24%

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OVERPAIR + FD VS BARE TWO PAIR ( ~50/50) Board


A♠Q♠A♣7♦ 51.10% K♥9♣8♣2♦ 48.90%

OVERPAIR + FD VS PAIR + NFD Board

6♥ 8♥ 2♠ Hand Equity

Q♥Q♦J♠3♥ 39.51% A♥J♥7♠6♦ 60.49%

Commentary: Bare overpairs are usually weak on two-tone flops. Dominating flush draws are very powerful.

TOP PAIR + OVERCARDS VS MID PAIR + LOWER SIDECARDS (~65/35) Board

K♣ 2♥ 7♦ Hand Equity AKQJ 66.27% 8765 33.73%

Commentary: Over-cards improve equity significantly but to be ahead of top pair you also need back-door flush/straight draws. Example: Board: T♣2♥3♦ T♥9♣7♦6♠ 48.17% A♣K♦Q♦3♣ 51.83%

PAIR + GOOD KICKERS VS PAIR + BAD KICKER (~67.5/32.5) Board

J♦ 6♥ 2♠ Hand Equity QJ83 29.62% AKJT 70.38%

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Board J♦ 6♥ 2♠

Hand Equity 8765 33.45% QT96 66.55%

Board J♦ 6♥ 2♠

Hand Equity QJ98 35.97% AKTJ 64.03%

PAIR VS 4 OVERCARDS (~60/40) Board

T♦ 3♥ 2♠ Hand Equity T987 59.60% AKQJ 40.40%

PAIR VS BARE FLUSH DRAW + BD STR DRAWS Board

K♣ 2♣ 7♦ Hand Equity

K♠Q♠8♥5♥ 56.89% Q♦T♠8♣5♣ 43.11%

PAIR VS 13-CARD WRAP (~50/50) Board

K♠ 4♥ 7♦ Hand Equity

K♣Q♦J♠9♠ 48.66% J♥8♣6♥5♣ 51.34%

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TWO PAIR MATCH-UPS

TWO PAIR VS 13-CARD WRAP (~55/45) Board

K♠ 4♥ 7♦ Hand Equity

K♣Q♦J♠7♠ 54.88% J♥8♣6♥5♣ 45.12%

TWO PAIR VS 13-CARD WRAP + FD (~45/55) Board

K♠ 4♥ 7♥ Hand Equity

K♣Q♦J♠7♠ 43.54% J♥8♣6♥5♣ 56.46%

TWO PAIR VS 13-CARD WRAP + FD + PAIR (~40/60) Board

T♦ 7♠ 2♦ Hand Equity

K♦J♣T♠7♥ 37.87% J♠9♦8♦2♥ 62.13%

TWO PAIR + OVERS VS TWO PAIR + UNDERS (~65/35) Board

Q♠ 6♥ 8♥ Hand Equity

A♦K♠Q♣8♠ 66.83% Q♦8♦3♥2♣ 33.17%

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TWO PAIR VS PAIR + FD (~50/50) Board

Q♠ 6♥ 8♥ Hand Equity

A♠Q♣6♦2♠ 49.02% K♥Q♥J♦3♦ 50.98%

Board Q♠ 6♥ 8♥

Hand Equity A♠Q♣6♦2♠ 51.22% K♥J♦8♦5♥ 48.78%

BARE TOP TWO VS BOTTOM SET (~20/80) Board

T♣ 7♠ 2♦ Hand Equity

T♠7♥4♦3♣ 21.95% Q♥Q♦2♠2♥ 78.05%

TOP TWO + 2 BDFD + BD STRAIGHT DRAWS VS BARE BOTTOM SET

(~30/70) Board

T♣ 7♠ 2♦ Hand Equity

Q♦ J♠T♠7♦ 31.95% 3♥3♦2♠2♥ 68.05%

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TRIPS

STRONG TRIPS VS WEAK TRIPS (~65/35) Board

6♠ 6♦ 9♣ Hand Equity AKQ6 67.86% 6534 32.14%

Commentary: Having a pair decreases your equity by ~5.00% if you are ahead (AAQ6 would have 63.05%). It decreases your equity by about ~10.00% if you’re already behind and your opponent doesn’t have a pair himself.

TRIPS + OVERCARDS VS MADE FULL HOUSE (~60/40) Board

9♠ 8♦ 9♣ Hand Equity AKQ9 39.53% 9832 60.47%

Commentary: Each clean overcard is worth ~12.00%.

TRIPS VS UNDER-FULL (~42/58) Board

9♠ 8♦ 9♣ Hand Equity AKQ9 42.17% 8867 57.83%

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TRIPS VS OVERPAIR + FLUSH DRAW (~70/30) Board

9♠ 8♠ 9♣ Hand Equity 9532 68.63%

A♠A♣Q♠4♣ 31.37%

TRIPS VS 13-CARD WRAP (~60/40) Board

9♠ 6♠ 9♣ Hand Equity

9♥4♣3♦2♠ 58.54% A♦T♠8♣7♦ 41.46%

Commentary: A flush draw only improves your equity by about 5.00% because of drawing dead on turn plus re-drawing factor.

TRIPS VS OESD + NFD (~60/40) Board

9♠ 6♠ 9♣ Hand Equity 9432 62.31%

A♠Q♠8♣7♣ 37.69% Commentary: Blockers can improve you trips dramatically, for example A♥T♥9♣5♠ would have 72.80% on the same board.

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13-CARD WRAPS

13-CARD WRAP VS ONE PAIR (~55/45) Board

Q♥ 3♦ 4♠ Hand Equity

8♦7♦6♠5♠ 55.00% Q♣J♠9♠8♣ 45.00%

13-CARD WRAP + PAIR VS ONE PAIR (~60/40) Board


7♦6♠5♠4♦ 60.85% Q♣J♠9♠8♣ 39.15%

13-CARD WRAP + PAIR VS TWO PAIR (~50/50) Board


7♦6♠5♠4♦ 50.00% Q♣J♠9♠4♣ 50.00%

13-CARD WRAP + PAIR VS PAIR + FD (~40/60) Board

Q♥ 3♦ 4♥ Hand Equity

7♦6♠5♠4♦ 38.05% Q♣J♠9♥8♥ 61.95%

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13-CARD WRAP NO PAIR VS PAIR + FD (~30/70) Board

Q♥ 3♦ 4♥ Hand Equity

8♦7♦6♠5♠ 31.95% Q♣J♠9♥8♥ 68.05%

13-CARD WRAP VS SETS (~40/60) Board


8♣7♦6♠5♠ 40% Q♣Q♠T♣9♠ 60%

13-CARD WRAP + NFD VS SET (~50/50) Board

Q♥ 3♦ 4♦ Hand Equity

A♦7♦6♠5♠ 50.37% Q♣Q♠T♣9♠ 49.63%

13-CARD WRAP + PAIR VS OESD + FD + OVERCARD (~45/55) Board


J♥T♦9♣7♥ 45.43% K♠T♥9♠3♦ 54.57%

13-CARD WRAP VS OVERPAIR ON TRIPS (~35/65) Board

3♠ 2♦ 3♣ Hand Equity

K♣5♣6♥4♦ 36.71% A♦A♠J♣9♣ 63.29%

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13-CARD WRAP VS STRAIGHT (~47/53) Board

J♥ 9♠ 7♦ Hand Equity KQT* 43.75% T8** 56.25%

Board T♥ 9♠ 7♦

Hand Equity KQJ* 50.91% 86** 49.09%

13-CARD (NUT) WRAP VS DOMINATED STRAIGHT DRAW (~65/35) Board

T♠ 9♣ 5♦ Hand Equity KQJ* 64.37% J87* 35.63%

Commentary: The nut 13-card wrap is a very powerful draw. Whenever there is a flush draw it is devalued significantly, especially if it does not also have a pair.

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FLUSH DRAWS

FLUSH DRAW VS STRAIGHT (~35/65) Board

J♠ T♠ Q♣ Hand Equity

8♦7♦6♠4♠ 35.61% A♦K♦3♠2♣ 64.39%

FLUSH DRAW + BD TWO PAIR/TRIPS VS OVERPAIR (~40/60) Board


Q♦T♠9♠8♥ 40.61% A♦A♠K♦J♣ 59.39%

FLUSH DRAW + OVERPAIR VS SUPER WRAP (~60/40) Board

6♥ 9♥ Q♠ Hand Equity

A♠A♥3♦2♥ 58.17% J♠T♦8♣7♦ 41.83%

FLUSH DRAW + OVERPAIR VS SET (~33/66) Board

J♠ 6♠ 2♣ Hand Equity

K♠K♣8♠3♦ 33.66% A♦J♦J♥3♥ 66.34%

Commentary: Add a BDFD and some BD Straight Draws: K♠K♣8♠7♣ 40.00%

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FLUSH DRAW + GUTSHOT VS TWO PAIR (~42.5/57.5) Board

Q♣ J♠ 2♠ Hand Equity

9♠8♠6♦7♦ 39.27% Q♥J♥4♥3♠ 60.73%

Board Q♣ J♠ 2♠

Hand Equity A♠T♠6♦7♦ 43.90% Q♠J♥8♥3♠ 56.10%

Board Q♣ J♠ 2♠

Hand Equity A♠K♠7♦6♦ 45.73% Q♠J♥8♥3♠ 54.27%

Commentary: Adding bottom pair to any of these simulations increases the flush draw’s equity by 10.00-15.00%.

FLUSH DRAW + TWO PAIR VS STRAIGHT (~55/45) Board

Q♣ T♠ 9♣ Hand Equity

Q♦T♣8♣2♦ 54.63% K♠J♥7♥6♥ 45.37%

Commentary: On a blank turn, Q♦T♣8♣2♦ drops to ~33.00%.

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MULTI-WAY POTS

OVERPAIR VS 13-CARD WRAP + FD VS TOP TWO PAIR Board

J♣ 2♣ 9♠ Hand Equity

A♠A♦7♥4♦ 11.41% Q♣T♦8♣7♠ 65.02% K♥J♦9♦4♥ 23.57%

OVERPAIR + NFD VS 13-CARD WRAP + FD VS TOP TWO PAIR Board


A♣A♦7♥4♣ 39.94% Q♣T♦8♣7♠ 35.14% K♥J♦9♦4♥ 24.92%

OVERPAIR VS TOP PAIR + FLUSH DRAW VS MIDDLE PAIR + NFD Board

Q♣ 7♠ 2♠ Hand Equity

A♣A♦T♥4♦ 21.77% K♠Q♦J♦8♠ 26.43% A♠7♦6♠5♥ 51.80%

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PAIR + 13-CARD STRAIGHT DRAW + BDFD VS DOMINATED 13-CARD

WRAP + FD VS TOP TWO PAIR Board


K♠Q♠J♥T♣ 24.47% Q♣T♦8♣7♠ 43.54% K♥J♦9♦4♥ 31.98%

TWO PAIR VS FLUSH DRAW VS 13-CARD WRAP Board

9♣ 7♠ 2♠ Hand Equity

A♦K♦9♠7♦ 32.88% K♠Q♦5♦3♠ 34.08% J♣T♦8♠4♣ 33.03%

SET VS FLUSH DRAW VS 13-CARD WRAP Board


K♦9♠9♦7♦ 44.59% K♠Q♦5♦3♠ 27.48% J♣T♦8♠4♣ 27.93%

TWO PAIR VS FLUSH DRAW VS STRAIGHT Board


A♦K♦9♠7♦ 21.32% K♠Q♦5♦3♠ 30.78% J♣T♦8♠4♣ 47.90%

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SET VS FLUSH DRAW VS STRAIGHT Board


K♦9♠9♦7♦ 35.29% K♠Q♦5♦3♠ 26.58% J♣T♦8♠4♣ 38.14%

13-CARD WRAP VS TOP TWO VS INFERIOR 13-CARD + PAIR Board

J♣ 9♠ 2♦ Hand Equity

K♣Q♥T♥3♣ 42.87% A♦K♦J♠9♦ 40.24% J♥T♠8♥7♠ 16.89%

Commentary: In multi-way pots, live back-door flush draws improve your equity by ~4.00% (8♥7♠T♦J♥ in the same simulation only has 12.01% equity. The 13-CARD WRAP picks almost all of these extra points, going up to 47.30%). Commentary: Live flush draws are very important in multi-way pots.

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PREPRE -- FLOP EQUITYFLOP EQUITY

AA, KK, BROADWAY HANDS

PRE-FLOP Hand Equity

AA**, KK**, BBBB

60.76%

JT98 39.24%


AA**, KK**, BBBB

64.62%

AKJ9 35.38%


AA**, KK**, BBBB

59.10%

5678 40.90%


AA**, KK**, BBBB

66.29%

TT85 33.71%


AA**, KK**, BBBB

60.15%

6677 39.85%

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LOW RUNDOWNS VS BIG PAIRS

BIG PAIR VS RAINBOW LOW RUNDOWN PRE-FLOP

Hand Equity AA**, KK**,

QQ** 62.62%

7♠6♣5♥4♦ 37.38%

BIG PAIRS VS SINGLE-SUITED LOW RUNDOWN PRE-FLOP


QQ** 59.50%

7♠6♥5♣4♠ 40.50%

BIG PAIRS VS DOUBLE-SUITED LOW RUNDOWN PRE-FLOP


QQ** 56.30%

7♣6♣5♠4♠ 43.70%

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KK HANDS PRE-FLOP

Hand Equity KK** 62.51% **** 37.49%

PRE-FLOP Hand Equity KK** 55.92% A*** 44.08%

PRE-FLOP Hand Equity KK** 54.82% 20% 45.18%

PRE-FLOP Hand Equity KK** 48.35% 10% 51.65%


K♠K♣J♠T♣ 53.95% 10% 46.05%


A♠K♣K♠T♣ 59.21% 10% 40.79%

Commentary: KK** doesn’t do well against a tight 3betting range. Connectedness and suitedness add considerable equity. Kings will get its equity value from opponents playing lower pocket pairs and off-suit hands. AKK* is much stronger than other KK** hands because it lowers the chances of running into AA dramatically and it also out-kicks other A*** hands when an Ace flops. As we saw before, the nut flush draw will also add a lot of value to a hand.

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Post-flop Tables Implied Odds given pot-‐sized turn and river bets

Payoff Frequency

Outs 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 -$110 -$110 -$110 -$100 -$100 -$100 -$100 -$100 -$100 -$100 -$100 1 -$93 -$92 -$91 -$90 -$90 -$89 -$88 -$87 -$87 -$86 -$85 2 -$85 -$84 -$82 -$81 -$79 -$78 -$76 -$75 -$73 -$72 -$70 3 -$78 -$75 -$73 -$71 -$69 -$66 -$64 -$62 -$60 -$57 -$55 4 -$70 -$67 -$64 -$61 -$58 -$55 -$52 -$49 -$46 -$43 -$40 5 -$62 -$59 -$55 -$51 -$48 -$44 -$40 -$36 -$33 -$29 -$25 6 -$55 -$51 -$46 -$42 -$37 -$33 -$28 -$24 -$19 -$15 -$10 6.5 -$51 -$46 -$42 -$37 -$32 -$27 -$22 -$17 -$12 -$4 -$3 7 -$48 -$42 -$37 -$32 -$27 -$21 -$16 -$11 -$6 $0 $5 7.5 -$44 -$38 -$33 -$27 -$21 -$16 -$10 -$4 $1 $7 $13 8 -$40 -$34 -$28 -$22 -$16 -$10 -$4 $2 $8 $14 $20 8.5 -$36 -$30 -$24 -$17 -$11 -$4 $2 $8 $15 $21 $28 9 -$33 -$26 -$19 -$12 -$6 $1 $8 $15 $22 $28 $35 9.5 -$29 -$22 -$15 -$7 $0 $7 $14 $21 $28 $35 $43 10 -$25 -$18 -$10 -$3 $5 $13 $20 $28 $35 $43 $50 10.5 -$21 -$13 -$6 $2 $10 $18 $26 $34 $42 $50 $58 11 -$18 -$9 -$1 $7 $16 $24 $32 $40 $50 $57 $65 11.5 -$14 -$5 $4 $12 $21 $29 $38 $47 $55 $64 $73 12 -$10 -$1 $8 $17 $26 $35 $44 $53 $62 $71 $80 13 -$3 $7 $17 $27 $37 $46 $56 $66 $76 $85 $95 14 $5 $16 $26 $37 $47 $58 $68 $79 $89 $100 $110 15 $13 $24 $35 $46 $58 $69 $80 $91 $103 $104 $125

Commentary: Assuming a reasonable amount of money behind, the implied odds decision is most worth thinking about when we have somewhere in the range of 8-10 outs. Any more than that and we willl usually have a clear call. Source: Advanced PLO Theory by Tom Chambers

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Required Fold frequency – All-In Semi-bluff Bet Bet Size (% of pot) Equity 50% 60% 70% 80% 90% 100% 110% 120% 0% 33% 38% 41% 44% 47% 50% 52% 55% 5% 29% 33% 37% 40% 43% 46% 48% 51% 10% 23% 28% 32% 35% 38% 41% 44% 46% 15% 17% 21% 25% 29% 32% 35% 38% 41% 20% 9% 14% 18% 22% 25% 29% 32% 34% 25% n/a 5% 9% 13% 17% 20% 23% 26% 30% n/a n/a n/a 2% 6% 9% 12% 15% 35% n/a n/a n/a n/a n/a n/a n/a 1% 40% n/a n/a n/a n/a n/a n/a n/a n/a Bet Size (% of pot) Equity 130% 140% 150% 160% 170% 180% 190% 200% 0% 57% 58% 60% 62% 63% 64% 66% 67% 5% 53% 55% 57% 58% 60% 61% 62% 64% 10% 48% 50% 52% 54% 56% 57% 59% 60% 15% 43% 45% 47% 49% 51% 53% 54% 56% 20% 37% 39% 41% 43% 45% 47% 48% 50% 25% 29% 31% 33% 35% 38% 39% 41% 43% 30% 18% 21% 23% 25% 28% 30% 32% 33% 35% 4% 7% 9% 12% 14% 16% 18% 20% 40% n/a n/a n/a n/a n/a n/a n/a n/a Commentary: These two tables display the frequency with which our opponents have to fold for our semi-bluffs to turn a profit, given what percetnage of the pot we shove all-in for, and how much pot equity we have. We cover this extensively in the PLO QuickPro lessons, but I included this table to remind you how integral semi-bluffing is to your success as a PLO player. Here, notice how infrequently our bluffs have to work when we supplement our fold equity with some pot equity. These concepts are most applicable in three-bet pots facing a c-bet, semi-bluffing the turn against an aggressive player, or semi-bluff check/raising the turn. Source: Advanced PLO Theory by Tom Chambers

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